Carey - Organic Chemistry - chapt03

Carey - Organic Chemistry - chapt03

(Parte 1 de 5)

CHAPTER 3

Hydrogen peroxide is formed in the cells of plants and animals but is toxic to them.

Consequently, living systems have developed mechanisms to rid themselves of hydrogen peroxide, usually by enzyme-catalyzed reduction to water. An understanding of how reactions take place, be they reactions in living systems or reactions in test tubes, begins with a thorough knowledge of the structure of the reactants, products, and catalysts. Even a simple molecule such as hydrogen peroxide may be structurally more complicated than you think. Suppose we wanted to write the structural formula for

H2O2in enough detail to show the positions of the atoms relative to one another. We could write two different planar geometries Aand B that differ by a 180°rotation about the O±O bond. We could also write an infinite number of nonplanar structures, of which C is but one example, that differ from one another by tiny increments of rotation about the O±O bond.

Structures A, B, and C represent different conformationsof hydrogen peroxide.

Conformations are different spatial arrangements of a molecule that are generated by rotation about single bonds.Although we can’t tell from simply looking at these structures, we now know from experimental studies that C is the most stable conformation.

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In this chapter we’l examine the conformations of various alkanes and cycloalkanes, focusing most of our attention on three of them: ethane, butane,and cyclohexane. Adetailed study of even these three will take us a long way toward understanding the main ideas of conformational analysis.

The conformation of a molecule affects many of its properties. Conformational analysis is a tool used not only by chemists but also by researchers in the life sciences as they attempt to develop a clearer picture of how molecules—as simple as hydrogen peroxide or as complicated as DNA—behave in biological processes.

3.1CONFORMATIONAL ANALYSIS OF ETHANE

Ethane is the simplest hydrocarbon that can have distinct conformations. Two, the staggered conformationand the eclipsed conformation,deserve special attention and are illustrated in Figure 3.1. The C±H bonds in the staggered conformation are arranged so that each one bisects the angle made by a pair of C±H bonds on the adjacent carbon. In the eclipsed conformation each C±H bond is aligned with a C±H bond on the adjacent carbon. The staggered and eclipsed conformations interconvert by rotation around the carbon–carbon bond. Different conformations of the same molecule are sometimes called conformersor rotamers.

Among the various ways in which the staggered and eclipsed forms are portrayed, wedge-and-dash, sawhorse, and Newman projection drawings are especially useful. These are shown for the staggered conformation of ethane in Figure 3.2 and for the eclipsed conformation in Figure 3.3.

We used wedge-and-dashdrawings in earlier chapters, and so Figures 3.2aand 3.3aare familiar to us. Asawhorsedrawing (Figures 3.2band 3.3b) shows the conformation of a molecule without having to resort to different styles of bonds. In a Newman projection(Figures 3.2cand 3.3c), we sight down the C±C bond, and represent the front carbon by a point and the back carbon by a circle. Each carbon has three substituents that are placed symmetrically around it.

90CHAPTER THREEConformations of Alkanes and Cycloalkanes

Eclipsed conformation of ethane Staggered conformation of ethane

FIGURE 3.1 The staggered and eclipsed conformations of ethane shown as ball-and-spoke models (left) and as space-filling models (right).

Newman projections were devised by Professor Melvin S. Newman of Ohio State University in the 1950s.

Learning By Modeling contains an animation showing the rotation about the O±O bond in hydrogen peroxide.

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PROBLEM 3.1Identify the alkanes corresponding to each of the drawings shown.

(a) (c)

(b) (d)

SAMPLE SOLUTION(a)The Newman projection of this alkane resembles that of ethane except one of the hydrogens has been replaced by a methyl group. The

The structural feature that Figures 3.2 and 3.3 illustrate is the spatial relationship between atoms on adjacent carbon atoms. Each H±C±C±H unit in ethane is characterized by a torsion angleor dihedral angle, which is the angle between the H±C±C

CH2CH3

CH2CH3 CH3

CH3

CH3

CH3H H H

(a) Wedge-and-dash H

H (c) Newman projection

FIGURE 3.2Some commonly used representations of the staggered conformation of ethane.

FIGURE 3.3Some commonly used representations of the eclipsed conformation of ethane.

BackForwardMain MenuTOCStudy Guide TOCStudent OLCMHHE Website plane and the C±C±H plane. The torsion angle is easily seen in a Newman projection of ethane as the angle between C±H bonds of adjacent carbons.

Eclipsed bonds are characterized by a torsion angle of 0°. When the torsion angle is approximately 60°, we say that the spatial relationship is gauche;and when it is 180° we say that it is anti.Staggered conformations have only gauche or anti relationships between bonds on adjacent atoms.

Of the two conformations of ethane, the staggered is more stable than the eclipsed.

The measured difference in potential energy between them is 12 kJ/mol (2.9 kcal/mol). Asimple explanation has echoes of VSEPR (Section 1.10). The staggered conformation allows the electron pairs in the C±H bonds of one carbon to be farther away from the electron pairs in the C±H bonds of the other than the eclipsed conformation allows. Electron-pair repulsions on adjacent carbons govern the relative stability of staggered and eclipsed conformations in much the same way that electron-pair repulsions influence the bond angles at a central atom.

The destabilization that comes from eclipsed bonds on adjacent atoms is called torsional strain.Torsional strain is one of several structural features resulting from its three-dimensional makeup that destabilize a molecule. The total strain of all of the spatially dependent features is often called steric strain.Because three pairs of eclipsed bonds produce 12 kJ/mol (2.9 kcal/mol) of torsional strain in ethane, it is reasonable to assign an “energy cost” of 4 kJ/mol (1 kcal/mol) to each pair of eclipsed bonds.

In principle there are an infinite number of conformations of ethane, differing by only tiny increments in their torsion angles. Not only is the staggered conformation more stable than the eclipsed, it is the most stable of all of the conformations; the eclipsed is the least stable. Figure 3.4 shows how the potential energy of ethane changes for a 360° rotation about the carbon–carbon bond. Three equivalent eclipsed conformations and three equivalent staggered conformations occur during the 360°rotation; the eclipsed conformations appear at the highest points on the curve (potential energy maxima), the staggered ones at the lowest (potential energy minima).

PROBLEM 3.2Find the conformations in Figure 3.4 in which the red circles are (a) gauche and (b) anti.

Diagrams such as Figure 3.4 can be quite helpful for understanding how the potential energy of a system changes during a process. The process can be a simple one such as the one described here—rotation around a carbon–carbon bond. Or it might be more complicated—a chemical reaction, for example. We will see applications of potential energy diagrams to a variety of processes throughout the text.

Let’s focus our attention on a portion of Figure 3.4. The region that lies between a torsion angle of 60°and 180°tracks the conversion of one staggered conformation of

Torsion angle 180° Anti

Torsion angle 60° Gauche

Torsion angle 0° Eclipsed

92CHAPTER THREEConformations of Alkanes and Cycloalkanes

Stericis derived from the Greek word stereosfor “solid” and refers to the three-dimensional or spatial aspects of chemistry.

The animation on the Learning By ModelingCD shows rotation about the C±C bond in ethane.

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ethane to the next one. Both staggered conformations are equivalent and equal in energy, but for one staggered conformation to get to the next, it must first pass through an eclipsed conformation and needs to gain 12 kJ/mol (2.9 kcal/mol) of energy to reach it.

This amount of energy is the activation energy(Eact) for the process. Molecules must become energized in order to undergo a chemical reaction or, as in this case, to undergo rotation around a carbon–carbon bond. Kinetic (thermal) energy is absorbed by a molecule from collisions with other molecules and is transformed into potential energy. When the potential energy exceeds Eact, the unstable arrangement of atoms that exists at that instant can relax to a more stable structure, giving off its excess potential energy in col- lisions with other molecules or with the walls of a container. The point of maximum potential energy encountered by the reactants as they proceed to products is called the transition state.The eclipsed conformation is the transition state for the conversion of one staggered conformation of ethane to another.

Rotation around carbon–carbon bonds is one of the fastest processes in chemistry.

Among the ways that we can describe the rate of a process is by its half-life,which is the length of time it takes for one half of the molecules to react. It takes less than 10 6 seconds for half of the molecules in a sample of ethane to go from one staggered conformation to another at 25°C. At any instant, almost all of the molecules are in staggered conformations; hardly any are in eclipsed conformations.

As with all chemical processes, the rate of rotation about the carbon–carbon bond increases with temperature. The reason for this can be seen by inspecting Figure 3.5, where it can be seen that most of the molecules in a sample have energies that are clustered around some average value; some have less energy, a few have more. Only mole- cules with a potential energy greater than Eact, however, are able to go over the transition state and proceed on to products. The number of these molecules is given by the shaded areas under the curve in Figure 3.5. The energy distribution curve flattens out at higher temperatures, and a greater proportion of molecules have energies in excess of

Eactat T2(higher) than at T1(lower). The effect of temperature is quite pronounced; an increase of only 10°C produces a two- to threefold increase in the rate of a typical chem- ical process.

Potential energy, kcal/molPotential energy, kJ/mol

2.9 kcal/mol12 kJ/mol

The structure that exists at the transition state is sometimes referred to as the transition structureor the activated complex.

FIGURE 3.4Potential energy diagram for rotation about the carbon–carbon bond in ethane. Two of the hydrogens are shown in red and four in green so as to indicate more clearly the bond rotation.

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3.2CONFORMATIONAL ANALYSIS OF BUTANE

The next alkane that we examine is butane. In particular, we consider conformations related by rotation about the bond between the middle two carbons

(CH3CH2±CH2CH3). Unlike ethane, in which the staggered conformations are equivalent, two different staggered conformations occur in butane, shown in Figure 3.6. The methyl groups are gauche to each other in one, anti in the other. Both conformations are staggered, so are free of torsional strain, but two of the methyl hydrogens of the gauche conformation lie within 210 pm of each other. This distance is less than the sum of their van der Waals radii (240 pm), and there is a repulsive force between them. The destabilization of a molecule that results when two of its atoms are too close to each other is

94CHAPTER THREEConformations of Alkanes and Cycloalkanes

Fraction of molecules having a particular energy

Eact Energy

FIGURE 3.5Distribution of molecular energies. (a) The number of molecules with energy greater than Eactat temperature T1is shown as the darker-green shaded area. (b) At some higher temperature T2, the shape of the energy distribution curve is different, and more molecules have energies in excess of Eact.

CH3

CH3

CH3

CH3HH H

FIGURE 3.6The gauche and anti conformations of butane shown as ball-and-spoke models (left) and as Newman projections (right). The gauche conformation is less stable than the anti because of the van der Waals strain between the methyl groups.

BackForwardMain MenuTOCStudy Guide TOCStudent OLCMHHE Website called van derWaals strain,or steric hindranceand contributes to the total steric strain. In the case of butane, van der Waals strain makes the gauche conformation approximately 3.2 kJ/mol (0.8 kcal/mol) less stable than the anti.

Figure 3.7 illustrates the potential energy relationships among the various conformations of butane. The staggered conformations are more stable than the eclipsed. At any instant, almost all the molecules exist in staggered conformations, and more are present in the anti conformation than in the gauche. The point of maximum potential energy lies some 25 kJ/mol (6.1 kcal/mol) above the anti conformation. The total strain in this structure is approximately equally divided between the torsional strain associated with three pairs of eclipsed bonds (12 kJ/mol; 2.9 kcal/mol) and the van der Waals strain between the methyl groups.

PROBLEM 3.3Sketch a potential energy diagram for rotation around a carbon–carbon bond in propane. Clearly identify each potential energy maximum and minimum with a structural formula that shows the conformation of propane at that point. Does your diagram more closely resemble that of ethane or of butane? Would you expect the activation energy for bond rotation in propane to be more than or less than that of ethane? Of butane?

Potential energy, kcal/mol3 kJ/mol

Potential energy, kJ/mol

14 kJ/mol

FIGURE 3.7Potential energydiagram for rotation around the central carbon–carbon bond in butane.

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96CHAPTER THREEConformations of Alkanes and Cycloalkanes MOLECULAR MECHANICS APPLIED TO ALKANES AND CYCLOALKANES

Of the numerous applications of computer technology to chemistry, one that has been enthusiastically embraced by organic chemists examines molecular structure from a perspective similar to that gained by manipulating molecular models but with an additional quantitative dimension. Molecular mechanicsis a computational method that allows us to assess the stability of a molecule by comparing selected features of its structure with those of ideal “unstrained” standards. Molecular mechanics makes no attempt to explain why the van der Waals radius of hydrogen is 120 pm, why the bond angles in methane are 109.5°, why the C±C bond distance in ethane is 153 pm, or why the staggered conformation of ethane is 12 kJ/mol more stable than the eclipsed, but instead uses these and other experimental observations as benchmarks to which the corresponding features of other substances are compared.

If we assume that there are certain “ideal” values for bond angles, bond distances, and so on, it follows that deviations from these ideal values will destabilize a particular structure and increase its potential energy. This increase in potential energy is referred to as the strain energyof the structure. Other terms include steric energyand steric strain.Arith- metically, the total strain energy (Es) of an alkane or cycloalkane can be considered as

(Parte 1 de 5)

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